Methods of Calibrating a Clock Using Multiple Clock Periods with a Single Counter and Related Devices and Methods

ABSTRACT

A method of calibrating a first clock signal using a second clock signal and a plurality of calibration periods may include generating incremented counter values at a counter responsive to edges of the second clock signal. For at least two of the plurality of calibration periods, an initial incremented counter value from the counter may be stored in memory at an initial edge of the first clock signal for the respective calibration period, a final incremented counter value may be stored in memory at a final edge of the clock signal for the respective calibration period, and the at least two of the plurality of calibration periods may be overlapping with different initial and final edges of the first clock signal. For each of the plurality of calibration periods, a number of edges of the second clock signal occurring during the respective calibration period may be determined using the initial and final incremented counter values stored in memory. A relationship between the first and second clock signals may be determined using a sum of a number of edges of the second clock signal occurring during each of the plurality of calibration periods and using a sum of a number of first clock signal cycles occurring during each of the plurality of calibration periods.

FIELD OF THE INVENTION

The present invention relates generally to the field of electronics, andmore particularly, to methods of calibrating electronic clocks andrelated devices.

BACKGROUND

There is a wide variety of digital communication systems, some presentlyin existence, and some still under development. Digital communicationsystems include time-division multiple access (TDMA) systems, such ascellular radio telephone systems that comply with the Global System forMobile communications (GSM) telecommunication standard and itsenhancements like GSM/EDGE, and Code-Division Multiple Access (CDMA)systems, such as cellular radio telephone systems that comply with theIS-95, cdma2000, and Wideband CDMA (WCDMA) telecommunication standards.Digital communication systems also include “blended” TDMA and CDMAsystems, such as cellular radio telephone systems that comply with theUniversal Mobile Telecommunications System (UMTS) standard, whichspecifies a third generation (3G) mobile system being developed by theEuropean Telecommunications Standards Institute (ETSI) within theInternational Telecommunication Union's (ITU's) IMT-2000 framework. TheThird Generation Partnership Project (3GPP) promulgates the UMTSstandard. High Speed Downlink Packet-data Access (HSDPA) is an evolutionof WCDMA specified in the Release 5 version of the 3GPP WCDMAspecification. The 3GPP has begun considering the next major step orevolution of the 3G standard (sometimes called Super 3G—“S3G”) to ensurethe long-term competitiveness of 3G.

Other types of digital communication systems allow equipment tocollaborate with one another by means of wireless networks. Examplesinclude Wireless Local Area Network (WLAN) and Bluetooth equipment.

One thing that these different systems have in common is the need tomaintain accurate timing. In modern radio transceivers (e.g., WCDMA, GSMand S3G phones and WLAN and Bluetooth equipment), two different clocksare used: a system clock (SC) and a real-time clock (RTC). The SC isusually a high frequency clock, running at several MHz, and generated bya highly stable oscillator, often applying a temperature-controlledcrystal. The SC acts as the reference and is the frequency source forall radio related operations, such as radio frequency (RF) carriersynthesis. The crystals used for the SC have an accuracy on the order of20 parts per million (ppm). However, for cellular terminals, thisaccuracy is improved by locking the SC to the downlink signalstransmitted by the mobile network base stations. The SC is tuned to thedownlink signals and therefore inherits the better stability of theclock reference used in the base station, which is about 0.5 ppm.

The SC's stability is obtained at the expense of electrical currentconsumption. To run the SC, several of milliAmperes (mA) are required.In particular, the SC requires too much current when the transceiver isin idle mode or in a low-power mode in which it sleeps most of the time.Therefore, the SC is turned off during the sleep states. In order topreserve timing during such sleep states, each modern transceiver alsoincludes a non-reference clock, such as a low-power oscillator (LPO) orreal-time clock (RTC) which runs at a much lower level of currentconsumption (several tens to hundreds of micro Amperes). The RTC usuallyruns at a much lower frequency than the SC, typically several kHz.

The RTC is used for several timing operations in the cellular terminal.It controls the sleep periods, and determines such things as when theterminal has to wake up to monitor the paging control channel or scanother broadcast control channels. The RTC also determines for how longuplink synchronization with the network can be maintained. Uplinksynchronization is critical in time slotted systems, (i.e., systems thathave a TDMA component, such as GSM and the newly developed Long TermEvolution (LTE) for 3G systems (S3G)). Due to the unknown round-trippropagation delay between the terminal and the base station, timingadvance (TA) control messages need to be sent to the terminal in orderto align the receive timing of its uplink transmissions with the timingof other uplink transmissions. Clock drift is a general cause for uplinktiming mismatch, and requires the terminal to send uplink burstsfrequently so that the base station can measure the timing misalignmentand suitably command the terminal to adjust its timing by way of the TAmessage.

The inherent stability of the RTC is very poor, typically from 50 to 100ppm. However, its stability is improved by repeated calibrations. The SCis used as a stable reference during the calibration. Once the RTC iscalibrated, it has a level of stability close to the stability of theSC. In between calibration events, the stability remains within a fewppm.

U.S. Pat. No. 6,124,764 describes a calibration method that exploits theperiodic paging wake-up times. In particular, the LPO output signal ismonitored during a number of monitoring windows M. These windowspreferably correspond to the wake-up periods in the standby mode of thehost system that the LPO is part of. During wake-up periods, otheractivities such as page scanning, for example, may take place. Theresults of the monitoring process are accumulated. Based on theaccumulated result derived from M monitoring windows, a decision for thecorrection scheme is determined for the next period encompassing anotherM monitoring windows.

Conventional calibration techniques have a problem in that they requirequite a long calibration time. During the calibration, the SC has to runand this causes a high level of current consumption to be experienced.In order to limit the power consumption, the calibration duty cycle iskept low. However, this means that there is quite a long time betweenconsecutive calibration updates. During this time, the RTC may drift toofar away. Since the RTC controls the uplink timing, this drift willrequire uplink bursts to be sent to the base station frequently tosupport the TA procedure. The terminal expends power when it sends anuplink burst, and this reduces the terminal standby time. Furthermore,all of these uplink bursts increase overhead in the network.

SUMMARY

According to some embodiments of the present invention, a method ofcalibrating a first clock signal using a second clock signal and aplurality of calibration periods may include generating incrementedcounter values at a counter responsive to edges of the second clocksignal. For at least two of the plurality of calibration periods, aninitial incremented counter value from the counter at an initial edge ofthe first clock signal may be stored in memory for the respectivecalibration period, and a final incremented counter value at a finaledge of the first clock signal may be stored in memory for therespective calibration period. Moreover, the at least two of theplurality of calibration periods may be overlapping with differentinitial and final edges of the first clock signal. For each of theplurality of calibration periods, a number of edges of the second clocksignal occurring during the respective calibration period may bedetermined using the initial and final incremented counter values storedin memory. A relationship between the first and second clock signals maybe determined using a sum of a number of edges of the second clocksignal occurring during each of the plurality of calibration periods andusing a sum of a number of first clock signal cycles occurring duringeach of the plurality of calibration periods.

Determining the relationship may include determining a ratio using thesum of the number of edges of the second clock signal occurring duringeach of the plurality of calibration periods and using the sum of thenumber of first clock signal cycles occurring during each of theplurality of calibration periods. An initial edge of the first clocksignal for a first of the plurality of the calibration periods mayprecede an initial edge of the first clock signal for a second of theplurality of the calibration periods, the initial edge of the firstclock signal for the second of the plurality of the calibration periodsmay precede a final edge of the first clock signal for the first of theplurality of the calibration periods, and the final edge of the firstclock signal for the first of the plurality of the calibration periodsmay precede a final edge of the first clock signal for the second of theplurality of the calibration periods.

A same number of first clock cycles may occur during each of theplurality of calibration periods, and/or the plurality of calibrationperiods may include k calibration periods beginning at k consecutiveedges of the same transition type of the first clock (wherein k is apositive whole number). Generating incremented counter values mayinclude generating incremented counter values at the counter responsiveto edges of a same transition type of the second clock signal (with atransition type being either a rising or falling edge). Moreparticularly, the initial and final edges of the first clock signal maybe edges of a same transition type.

The second clock may be coupled to a receiver, and during first andsecond waking periods, the receiver may be operated using the secondclock. During a sleep period between the first and second wakingperiods, a duration of the sleep period may be timed using the firstclock with the second clock turned off.

According to other embodiments of the present invention, a method ofcalibrating a first clock signal using a second clock signal may includegenerating incremented counter values at a counter responsive to edgesof the second clock signal. For at least two different edges of thefirst clock signal, calculations may be performed based on respectiveincremented counter values. A relationship between the first and secondclock signals may be determined using linear regression using thecalculations based on the respective incremented counter values for theat least two different edges of the first clock signal.

Performing calculations based on the respective incremented countervalues may include performing the calculations based on the respectiveincremented counter values taken at edges of the same transition type ofrespective cycles of the first clock signal. Determining therelationship between the first and second clock signals using linearregression may include calculating a regression coefficient using theincremented counter values from the at least two different edges of thefirst clock signal. Performing calculations based on the respectiveincremented counter values may include integrating incremented countervalues taken at edges of the same transition type of different cycles ofthe first clock signal. The at least two different edges of the firstclock signal may include at least two consecutive edges of the firstclock signal of the same transition type.

At a first edge of the first clock signal, the counter and first andsecond adders may be set to initial values. At a second edge of thefirst clock signal after the first edge, an incremented counter valuegenerated by the counter may be added to the initial value of the firstadder to generate a second value of the first adder, and the initialvalue of the first adder may be added to the initial value of the secondadder to generate a second value of the second adder. At a third edge ofthe first clock signal after the second edge, an incremented countervalue generated by the counter may be added to the second value of thefirst adder to generate a third value of the first adder, and the secondvalue of the first adder may be added to the first value of the secondadder to generate a third value of the second adder.

The second clock may be coupled to a receiver, and during a first wakingperiod, the receiver may be operated using the second clock. During asleep period after the first waking period, a duration of the sleepperiod may be time using the first clock with the second clock turnedoff. During a second waking period after the sleep period, the receivermay be operated using the second clock.

According to still other embodiments of the present invention, a methodof calibrating a first clock signal using a second clock signal coupledto a receiver may include operating the receiver using the second clocksignal during a first waking period. For a first calibration periodduring the first waking period, a number of edges of the second clocksignal occurring during the first calibration period may be determined,and during a sleep period after the first waking period, a duration ofthe sleep period may be timed using the first clock signal with thesecond clock signal turned off. During a second waking period after thesleep period, the receiver may be operated using the second clocksignal, and for a second calibration period during the second wakingperiod, a number of edges of the second clock signal occurring duringthe second calibration period may be determined. A relationship betweenthe first and second clock signals may be determined using the number ofedges of the second clock signal occurring during the first interval andthe number of edges of the second clock signal occurring during thesecond interval.

Determining the relationship between the first and second clock signalsmay include calculating an average based on the number of edges of thesecond clock signal occurring during the first calibration period andthe number of edges of the second clock signal occurring during thesecond calibration period.

For a third calibration period during the first waking period, a numberof edges of the second clock signal occurring during the thirdcalibration period may be determined, and for a fourth calibrationperiod during the second waking period, a number of edges of the secondclock signal occurring during the fourth calibration period may bedetermined. Determining the relationship between the first and secondclock signals may include determining a first representation of therelationship between the first and second clock signals for the firstwaking period using the number of edges of the second clock signaloccurring during the first calibration period and the number of edges ofthe second clock signal occurring during the third calibration period. Asecond representation of the relationship between the first and secondclock signals for the second waking period may be determined using thenumber of edges of the second clock signal occurring during the secondcalibration period and the number of edges of the second clock signaloccurring during the fourth calibration period. After determining thefirst and second representations of the relationship between the firstand second clock signals, an aggregate representation of therelationship between the first and second clock signals may bedetermined using the first and second representations.

According to other embodiments of the present invention, determining therelationship between the first and second clock signals may includedetermining a first representation of the relationship between the firstand second clock signals using the number of edges of the second clocksignal occurring during the first calibration period and the number ofedges of the second clock signal occurring during the second calibrationperiod. A second representation of the relationship between the firstand second clock signals may be determined using the number of edges ofthe second clock signal occurring during the third calibration periodand the number of edges of the second clock signal occurring during thefourth calibration period. After determining the first and secondrepresentations of the relationship between the first and second clocksignals, an aggregate representation of the relationship between thefirst and second clock signals may be determined using the first andsecond representations. According to other embodiments of the presentinvention, determining the relationship between the first and secondclock signals may include performing linear regression using the numberof edges of the second clock signal occurring during the firstcalibration period, the number of edges of the second clock signaloccurring during the second calibration period, the number of edges ofthe second clock signal occurring during the third calibration period,and the number of edges of the second clock signal occurring during thefourth calibration period.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating a mobile communications deviceaccording to some embodiments of the present invention.

FIG. 2 is a block diagram of a calibration circuit that may be used tocount reference clock signal cycles for overlapping calibration periodsaccording to some embodiments of the present invention.

FIG. 3 is a timing diagram illustrating a reference clock signal and alow power clock signal as used to calibrate the low power clock signalaccording to some embodiments of the present invention.

FIG. 4 is a flow diagram illustrating operations of calibrating lowpower clock signal CSLP using reference clock signal CSR according tosome embodiments of the present invention.

FIG. 5 is a time line illustrating sleep periods (Sleep) and wakeperiods (W) for a mobile device according to some embodiments of thepresent invention.

FIG. 6 is a graph illustrating a relationship between incrementedcounter values and respective cycles of low power clock signal accordingto some embodiments of the present invention.

FIG. 7 is a timing diagram illustrating a reference clock signal and alow power clock signal as used to calibrate the low power clock signalusing linear regression according to some embodiments of the presentinvention.

FIG. 8 is a block diagram illustrating adding circuits that used toprovide summations for linear regression according to embodiments of thepresent invention.

FIG. 9 illustrates equations used to estimate frequencies according tosome embodiments of the present invention.

FIGS. 10-12 are graphs illustrating examples calibration errors as afunction of Δφ when calculating estimates of a frequency of low powerclock signal CSLP according to different embodiments of the presentinvention.

FIG. 13 is a table illustrating outputs of adding circuits of FIG. 8according to some embodiments of the present invention.

FIGS. 14 and 15 are flow charts illustrating operations of calibratinglow power clock signal CSLP using reference clock signal CSR accordingto some embodiments of the present invention.

FIG. 16 illustrates an equation used to estimate frequencies with linearregression according to some embodiments of the present invention.

DETAILED DESCRIPTION

Specific exemplary embodiments of the invention now will be describedwith reference to the accompanying drawings. This invention may,however, be embodied in many different forms and should not be construedas limited to the embodiments set forth herein. Rather, theseembodiments are provided so that this disclosure will be thorough andcomplete, and will fully convey the scope of the invention to thoseskilled in the art. In the drawing, like numbers refer to like elements.It will be understood that when an element is referred to as being“connected” or “coupled” to another element, it can be directlyconnected or coupled to the other element or intervening elements may bepresent. Furthermore, “connected” or “coupled” as used herein mayinclude wirelessly connected or coupled.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless expressly stated otherwise. Itwill be further understood that the terms “includes,” “comprises,”“including” and/or “comprising,” when used in this specification,specify the presence of stated features, integers, steps, operations,elements, and/or components, but do not preclude the presence oraddition of one or more other features, integers, steps, operations,elements, components, and/or groups thereof.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which this invention belongs. It will befurther understood that terms, such as those defined in commonly useddictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art andwill not be interpreted in an idealized or overly formal sense unlessexpressly so defined herein.

It will be understood that although the terms first and second are usedherein to describe various elements, these elements should not belimited by these terms. These terms are only used to distinguish oneelement from another element. As used herein, the term “and/or” includesany and all combinations of one or more of the associated listed items.The symbol “/” is also used as a shorthand notation for “and/or”.

Various embodiments of the present invention are described below withreference to block diagrams illustrating methods, apparatus and computerprogram products according to various embodiments of the invention. Itwill be understood that each block of the block diagrams and/oroperational illustrations, and combinations of blocks in the blockdiagrams and/or operational illustrations, can be implemented by analogand/or digital hardware, and/or computer program instructions. Thesecomputer program instructions may be provided to a processor of ageneral purpose computer, special purpose computer, ASIC, and/or otherprogrammable data processing apparatus, such that the instructions,which execute via the processor of the computer and/or otherprogrammable data processing apparatus, create means for implementingthe functions/acts specified in the block diagrams and/or operationalillustrations. Accordingly, it will be appreciated that the blockdiagrams and operational illustrations support apparatus, methods andcomputer program products.

FIG. 1 is a block diagram illustrating a mobile communications device101 (e.g., a mobile radiotelephone, a personal digital assistant or PDA,a handheld computer, a laptop computer, a notebook computer, etc.)according to some embodiments of the present invention. The mobilecommunications device 101 (also referred to as a mobile device) mayinclude a processor 103, a user interface 105, a calibration circuit107, a low power clock signal generator 109, a reference clock signalgenerator 111, a transceiver 115, and an antenna 117. The transceiver115 may include both a transmitter and a receiver to provide bothtransmission and reception of radio communications, the transceiver 115may include only a transmitter to provide only transmission of radiocommunications, or the transceiver 115 may include only a receiver toprovide only reception of radio communications. The user interface 105may include an image display (such as an LCD screen), a keypad, ajoystick, a dial, directional buttons, a touch sensitive image display,a speaker, a microphone, etc.

The reference clock signal generator 111 (also referred to as a systemclock) may include a highly stable oscillator configured to generate arelatively high frequency reference clock signal CSR used as a frequencysource for all radio related operations (such as radio frequency carriersynthesis) performed by the transceiver 115 during transmission and/orreception of radio signals. The reference clock signal CSR may have afrequency on the order of MHz (e.g., 26 MHz). Moreover, the referenceclock signal CSR may provide relatively high accuracy, for example, onthe order of 20 ppm (parts per million) or even 0.5 ppm.

The low power clock signal generator 109 (also referred to as alow-power oscillator or real-time clock) may be configured to generate arelatively low frequency low power clock signal CSLP used preservetiming during sleep mode operations of the mobile device 101. The lowpower clock signal CSLP may have a frequency on the order of kHz (e.g.,32 kHz). Moreover, the low power clock signal CSLP may providerelatively low accuracy. According to embodiments of the presentinvention, reference clock signal CSR may have a frequency that issignificantly greater than a frequency of low power clock signal CSLP.For example, a frequency of reference clock signal CSR may be at least100 times greater than a frequency of low power clock signal.

The processor 103 may process communications received from and/orcommunications to be transmitted through transceiver 115 responsive touser input received through user interface 105. The processor 103, forexample, may process voice communications, network communications (suchas Internet communications), text communications, data communications,etc. During periods of active communications (e.g., when radiocommunications are being transmitted/received through transceiver 115),the reference clock signal generator 111 may generate the relativelyhigh frequency reference clock signal CSR that is used by thetransceiver 115.

When the mobile device is not actively communicating using transceiver115, the mobile device 101 may operate in a low power sleep state withthe reference clock signal generator 111 turned off to conserve batterypower. During the sleep state, low power clock signal CSLP (generated bylow power clock signal generator 109) is used to preserve timing ofprocessor 103. During a low power sleep state, low power clock signalCSLP may be used to determine when processor 103, transceiver 115, andreference clock signal generator 111 should wake to monitor a pagingcontrol signal and/or to scan broadcast control channels.

Because an accuracy of low power clock signal CSLP may be relativelylow, calibration circuit 107 may be used to more accurately determine aperiod and/or frequency of low power clock signal CSLP using referenceclock signal CSR. By providing processor 103 with a more accuratedetermination of a period and/or frequency of low power clock signalCSLP, intervals between wake periods may be more accurately determinedto further conserve battery power. Methods used by calibration circuitsto determine a period and/or frequency of a low power clock signal CSLPare discussed in U.S. Pat. No. 7,272,078 to J. Haartsen entitled“Efficient Clock Calibration In Electronic Equipment,” the disclosure ofwhich is hereby incorporated herein in its entirety by reference. Whilethe calibration circuit 107 and processor 103 are illustrated asseparate blocks for the sake of clarity, it will be understood that someor all functions/elements of calibration circuit 107 may be included inprocessor 103 and/or other blocks of FIG. 1.

FIG. 2 is a block diagram of a calibration circuit 107A that may be usedto count reference clock signal CSR cycles (e.g., counting rising edgesor counting falling edges of the reference clock signal CSR) foroverlapping calibration periods using a single counter according to someembodiments of the present invention. As shown in FIG. 2, thecalibration circuit 107A may include a counter 201, memory 203(including a plurality of memory registers RS(1) to RS(n)), and a timingcontrol circuit 205.

Operations of the calibration circuit will be discussed in greaterdetail with reference to the timing diagram of FIG. 3. In particular,FIG. 3 is a timing diagram illustrating reference clock signal CSR andlow power clock signal CSLP as used to calibrate low power clock signalCSLP according to some embodiments of the present invention. During awaking period of communications device 101 including calibration circuit107A, transceiver 115 may be used to monitor a paging control signaland/or to scan broadcast control channels. Accordingly, reference clocksignal generator 111 may be turned on to generate reference clock signalCSR that is used by transceiver 115 (e.g., for radio frequency carriersynthesis). At the same time (during the waking period), the referenceclock signal CSR may also be used to calibrate the low power clocksignal CSLP.

As shown in FIG. 2, counter 201 may generate incremented counter valuesresponsive to rising edges of reference clock signal CSR. While countervalues are discussed by way of example as being incremented responsiveto rising edges of reference clock signal CSR, counter values could beincremented responsive to falling edges of reference clock signal CSRaccording to other embodiments of the present invention. As noted above,a frequency of clock signal CSR is significantly higher than a frequencyof low power clock signal CSLP. As discussed herein, an incrementedcounter value may incrementally increase responsive to each rising edgeof reference clock signal CSR. It will be understood, however, that anincremented counter value may incrementally decrease responsive to eachrising edge of reference clock signal CSR. Either way, a difference inincremented counter values at the beginning and end of a calibrationperiod may be used to determine a number of edges of a same transitiontype (e.g., either rising or falling) of reference clock signal CSR thatoccur during a calibration period (over a known number of cycles of lowpower clock signal CSLP). According to other embodiments of the presentinvention, counter values may be incremented responsive to rising andfalling edges of the reference clock signal CSR, for example, if thereference clock signal CSR has a 50% duty cycle. According to otherembodiments of the present invention, counter values may be incrementedresponsive to rising edges during some calibration windows (or wakingperiods), and counter values may be incremented responsive to fallingedges during other calibration windows (or waking periods).

Timing control circuit 205 may generate a reset signal for counter 201and write command and address information for memory 203 responsive tolow power clock signal CSLP. Before beginning calibration operationsduring a waking period, an output of counter 201 may be reset (e.g., tozero) responsive to a reset signal generated by timing control circuit205, and an output of counter 201 may be incremented responsive tosubsequent rising edges of reference clock signal CSR.

At different rising edges of the low power clock signal CSLP, respectiveincremented counter values P(1) to P(6) may be stored in respectivememory registers RS(1) to RS(6) of memory 203 responsive to writecommand and address information generated by timing control circuit 205.Pairs of incremented counter values (e.g., P(1) and P(4), P(2) and P(5),and P(3) and P(6)) for respective calibration periods (e.g., NSC_1,NSC_2, and NSC_3) may be stored in memory 203, and a difference betweeninitial and final values of a pair may define a number of rising edges(or a number of falling edges) of the reference clock signal during therespective calibration period.

By way of example, incremented counter values P(1), P(2), and P(3) maybe initial incremented counter values for first, second, and thirdcalibration periods NSC_1, NSC_2, and NSC_3, respectively, andincremented counter values P(4), P(5), and P(6) may be final incrementedcounter values for first, second, and third calibration periods NSC_1,NSC_2, and NSC_3, respectively. As shown in FIG. 3, initial incrementedcounter values P(1), P(2), and P(3) may be taken as outputs of counter201 at consecutive rising edges of low power clock signal CSLP; finalincremented counter values P(4), P(5), and P(6) may be taken as outputsof counter 201 at consecutive rising edges of low power clock signalCSLP; and a duration of each of calibration period NSC_1, NSC_2, andNSC_3 may be defined by a same number of cycles of low power clocksignal CSLP. According to other embodiments of the present invention,however, calibration periods may have different durations (e.g.,different numbers of cycles of low power clock signal CSLP), initialincremented counter values may be taken at non-consecutive rising edgesof the low power clock signal CSLP, and/or final incremented countervalues may be taken at non-consecutive rising edges of the low powerclock signal CSLP.

By providing that each of calibration periods NSC_1, NSC_2, and NSC_3has a same duration (measured as cycles of low power clock signal CSLP)known to processor 103, processor 103 can determine a frequencyrelationship between reference clock signal CSR and low power clocksignal CSLP using only incremented counter values P(1) to P(6) saved inrespective memory registers RS(1) to RS(6). While three calibrationperiods are discussed by way of example, any number of calibrationperiods may be used. If counter 201 is reset to 0 at the beginning ofcalibration period NSC_1, it may be unnecessary to save initial countervalue P(1) in memory 203 because a number of edges of reference clocksignal CSR occurring during calibration period NSC_1 will be equal tofinal counter value P(4).

Over a waking period, a number of edges (of a same transition type) ofreference clock signal CSR may be determined by processor 103 for eachof a plurality of overlapping calibration periods using initial andfinal incremented counter values P(1) to P(6) saved in memory registersRS(1) to RS(6). Accordingly, processor 103 can determine a relationshipαbetween a frequency FCSR of reference clock signal and a frequencyFCSLP such that:

FCSLP=αFCSR.

If NCSLP_i is the number of cycles of low power clock in a calibrationperiod i, NCSR_i is the number of edges of reference clock signal CSR ina calibration period i, and k is the number of calibration periods, therelationship α may be calculated as:

$\alpha = {\frac{\sum\limits_{i = {1{tok}}}N_{CSLP\_ i}}{\sum\limits_{i = {1{tok}}}N_{CSR\_ i}}.}$

If each calibration period has a same number NCSLP of cycles of lowpower clock signal CSLP, the summation from i=1 to K of NCSLP_i may becalculated as K*NCSLP. In the example of FIG. 3, k=3. Moreover, thesummation from i=1 to k of NCSR_i may be calculated as the summation ofdifferences between final and initial incremented counter values foreach calibration period. In the example of FIG. 3 the summation ofNCSR_i may be calculated as [P(4)−P(1)]+[P(5)−P(2)]+[P(6)−P(3)].

FIG. 4 is a flow diagram illustrating operations of calibrating lowpower clock signal CSLP using reference clock signal CSR according tosome embodiments of the present invention. Low power clock signal CSLPmay be considered a low speed clock and reference clock signal CSR maybe considered a high speed clock signal because a frequency of referenceclock signal CSR is significantly greater than a frequency of low powerclock CSLP. At block 401, incremented counter values may be generated atcounter 201 responsive to edges of reference clock signal CSR.

Over a waking period with both of low power clock signal CSLP andreference clock signal CSR on, initial and final incremented countervalues from counter 201 for a plurality of overlapping calibrationperiods NSC may be stored in respective memory registers RS of memory203 at block 403. For each of the plurality of calibration periods NSC,a number of edges of reference clock signal CSR occurring during therespective calibration period may be determined using the initial andfinal incremented counter values stored in memory 203 at block 404. Forexample, differences between initial and final counter values for eachof the calibration periods NSC may be used to determine a number ofedges of a same transition type of reference clock signal CSR occurringduring respective calibration periods NSC.

At block 405, processor 103 may determine a relationship betweenreference and low power clock signals CSR and CSLP using a sum of anumber of edges of reference clock signal CSR occurring during each ofthe plurality of calibration periods NSC and using a sum of a number oflow power clock signal CSLP cycles occurring during each of theplurality of calibration periods NSC. Determining the relationship, forexample, may include determining a ratio using the sum of the number ofedges of the reference clock signal CSR occurring during each of theplurality of calibration periods NSC and using the sum of the number oflow power clock signal CSLP cycles occurring during each of theplurality of calibration periods NSC. A same number of low power clockcycles may occur during each of the plurality of calibration periodsNSC, and the plurality of calibration periods may include k calibrationperiods beginning at k consecutive edges of the same transition type ofthe low power clock signal CSLP (where k is a positive whole number).

FIG. 5 is a time line illustrating sleep periods (Sleep) and wakeperiods (W) for mobile device 101 according to some embodiments of thepresent invention. More particularly, sleep periods between times t1 andt2, between times t3 and t4, and between times t5 and t6 (with referenceclock signal CSR off) may be relatively long compared to wake periodsbetween times t2 and t3, between times t4 and t5, and between times t6and t7 (with reference clock signal CSR on).

Operations discussed above with respect to FIGS. 2-4 may be performedduring each wake period when reference clock signal CSR is on so thatprocessor 103 may more accurately time sleep periods using low powerclock signal CSLP when reference clock signal CSR is off. By way ofexample, processor 103 can use the relationship α to more accuratelydetermine a frequency and/or period of low power clock signal CSLP, anda new relationship α may be determined at each wake period for useduring the subsequent sleep period without considering prior values ofα. According to other embodiments of the present invention, values ofα1, α2, α3, etc. from multiple wake periods may be combined to providean average α that is used to time sleep periods. For example, a movingaverage of individual values of α1, α2, α3, etc. may be used to providean average α, and/or a weighted average may be provided so that valuesof α for more recent wake periods are weighted more heavily in thecalculation of the average α. According to still other embodiments ofthe present invention, individual values of α1, α2, α3, etc. may becombined using exponential forgetting to provide a combined α.

According to additional embodiments of the present invention, therelationship α between reference clock signal CSR and low power clocksignal CSLP may be determined using linear regression. FIG. 6 is a graphillustrating an example of incremented counter values generated bycounter 201 (shown on the vertical y-axis) plotted against respectivecycles of low power clock signal CSLP (shown on the horizontal x-axis).More particularly, plots of the outputs P(1) to P(n) of counter 201(i.e., a number of edges of reference clock signal CSR shown as *) takenat a rising edge of each cycle n of low power clock signal CSLP withcounter 201 being reset to zero at a rising edge of low power clocksignal CSLP cycle zero (n=0) as shown in FIG. 7. The dashed line is anexample of a linear regression through the plotted counter valueoutputs. Accordingly, the slope of the dashed line (i.e., the regressioncoefficient) can be used to determine the relationship α between afrequency of low power clock signal CSLP and reference clock signal CSRsuch that:

FCSLP=αFCSR.

More particularly, a straight line for the data of FIG. 6 may bedetermined using a best fit (least mean square) regression analysis.While data for 10 consecutive cycles of low power clock signal CSLP isshown by way of example in FIG. 6, any number of samples may be takenover a wake period and/or samples corresponding to non-consecutivecycles of low power clock signal CSLP may be used.

Respective calculations of relationship α may thus be provided for aplurality of different waking periods W (shown in FIG. 5) using linearregression as discussed above. According to some embodiments of thepresent invention, the relationship α calculated during a wake period Wmay be used together with the low power clock signal CSLP to time thefollowing sleep period without considering calculations of therelationship α from other wake periods.

According to other embodiments of the present invention, calculations ofthe relationship α from multiple wake periods may be combined, and theresult of the combination may be used together with the low power clocksignal CSLP to time a sleep period. For example, calculations of therelationship α from a fixed number preceding of wake periods may beaveraged so that the combination is a moving average. Moreover, theindividual calculations of the relationship α may be weighted evenlywhen determining the average, or more recent calculations of therelationship α may be weighted more heavily than less recentcalculations when determining the average. In addition or in analternative, individual calculations of the relationship α may becombined using exponential forgetting.

According to still other embodiments of the present invention, data fromdifferent wake periods can be combined before performing regressionanalysis on the combined data. For example, counter values P(x, y) withsamples x (corresponding to low power clock signal cycles from 0 to n ina same wake period) taken from different wake periods y (from 0 to m)may be saved, and corresponding counter values from the different wakeperiods may be combined, for example, using averaging (moving, weighted,and/or non-weighted) and/or exponential forgetting. The results of thesecombinations may then be used to calculate the relationship α usinglinear regression. In other words, the following combinations can bemade:

Combine initial samples P(0, 0) to P(0, m) to provide combined samplePP(0);

Combine first samples P(1, 0) to P(1, m) to provide combined samplePP(1);

. . .

Combine first samples P(n−1, 1) to P(n−1, m) to provide combined samplePP(1);

Combine first samples P(n, 0) to P(n, m) to provide combined samplePP(n).

The relationship α can then be calculated by applying linear regressionto combined samples PP(0) to PP(n).

Operations of applying linear regression to counter values to determinea regression coefficient will now be discussed. As discussed above, thecounter 201 may generate incremented counter values P(i) responsive toedges (of a same transition type such as a rising edge) of referenceclock signal CSR which may have a frequency of about 26 MHz. The counter201 may be reset to an initial counter value P(0)=0 at a rising edge ofan initial cycle of the low power clock signal CSLP, and the counter 201may count to a final value P(N) on a rising edge of an N^(th) cycle oflow power clock signal CSLP. An estimate of the frequency of the lowpower clock signal CSLP may be calculated as:

$f_{{CSLP}{({estimate})}} = {\frac{N}{p(N)} \cdot {f_{CSR}.}}$

Because P(N) is an integer value, an error can be determined as:

$E = {\frac{f_{CSR}}{N \cdot f_{CSLP}}.}$

By using linear regression to estimate the relationship α betweenfrequencies of low power clock signal CSLP and reference clock signalCSR as discussed above, intermediate values P(i) may be used to increasean accuracy of calibration of low power clock signal CSLP.

When a straight line is fit to P(i) using linear regression as shown inFIG. 6, the relationship α may be determined as an inverse of aregression coefficient R of the line where:

$R = \frac{{\left( {N + 1} \right) \cdot {\sum\limits_{i = 0}^{N}{x \cdot y}}} - {\sum\limits_{i = 0}^{N}{x \cdot {\sum\limits_{i = 0}^{N}y}}}}{{\left( {N + 1} \right) \cdot {\sum\limits_{i = 0}^{N}x^{2}}} - {\sum\limits_{i = 0}^{N}{x \cdot {\sum\limits_{i = 0}^{N}x}}}}$$R = \frac{{\left( {N + 1} \right) \cdot {\sum\limits_{i = 0}^{N}{i \cdot {P(i)}}}} - {\sum\limits_{i = 0}^{N}{i \cdot {\sum\limits_{i = 0}^{N}{P(i)}}}}}{{\left( {N + 1} \right) \cdot {\sum\limits_{i = 0}^{N}i^{2}}} - {\sum\limits_{i = 0}^{N}{i \cdot {\sum\limits_{i = 0}^{N}i}}}}$${\sum\limits_{i = 0}^{N}i} = {\frac{N + 1}{2} \cdot N}$${\sum\limits_{i = 0}^{N}i^{2}} = {\frac{{2 \cdot N} + 1}{3} \cdot \frac{N + 1}{2} \cdot N}$

An estimation of the frequency of the low power clock signal CSLP can becalculated as f_(CSLP)=αf_(CSR), or using the formula illustrated inFIG. 16. Using the formulation of the regression coefficient R discussedabove and shown in FIG. 16, the summations may be implemented usingadding circuits as discussed below with respect to FIG. 8.

FIG. 8 is a block diagram illustrating adding circuits 801, 803, and 805that may be used in the calibration circuit of FIG. 1 to providesummations for a linear regression according to embodiments of thepresent invention. At an initial rising edge of low power clock signalCSLP beginning a calibration window, the registers P, IP, and IIP of therespective adding circuits 801, 803, and 805 may be reset to zero, andthe current value register P of adding circuit 801 may be incremented by1 at each successive rising edge of the reference clock signal CSR. Ateach successive rising edge of the low power clock signal CSLP(identifying successive cycles of CSLP), the current value of theregister IP is added to the current value of the register P and theresult is saved in the register IP. At each successive rising edge ofthe low power clock signal CSLP (identifying successive cycles of CSLP),the current value of the register IIP is added to the current value ofthe register IP and the result is saved in the register IIP.

While block 801 has been referred to as an adding circuit, block 801 mayalso be referred to as a counter. Moreover, the adding circuits 803 and805 may be referred to as integrators. In other words, the addingcircuit 803 integrates values generated by counter 801 at rising edgesof low power clock signal CSLP, and the adding circuit 805 integratesvalues generated by adding circuit 803 at rising edges of low powerclock signal CSLP.

After N cycles of the low power clock signal, the values of theregisters IP and IIP may be read by processor 103. The processor 103 maythen calculate an estimate of the frequency of low power clock signalCSLP using the equations provided in FIG. 9. FIG. 13 is a tableillustrating examples of values of registers P(i), IP(i), and IIP(i)over a 1.0 ms calibration window with a reference clock signal CSLPfrequency of 26 MHz, with low power clock signal frequency of 32 kHz,with a phase increment Δφ of 0.5, and with i indicating an elapsednumber of low power clock signals.

A calibration error may be a function of a phase offset φ0 and a phaseincrement Δφ. A phase offset φ0 is a difference in start phases ofreference clock signal CSR and low power clock signal CSLP. A phaseincrement Δφ is a non-integer part of a ratio between frequencies ofreference clock signal CSR and low power clock signal CSLP (a numberbetween −0.5 and 0.5).

If a period of low power clock signal CSLP is not an integer multiple ofa period of reference clock signal CSR, an estimation of a frequency oflow power clock signal CSLP may be better than if a period of low powerCSLP is an integer multiple of a period of reference clock signal CSR.Results of the linear regression may actually be improved, for example,if there is some non-linearity of the data points provided in FIG. 6.This effect may be demonstrated by calculating a calibration error as afunction of a phase offset φ0 (of reference clock signal CSR) and aphase increment Δφ (of reference clock signal CSR) per cycle of lowpower system clock CSLP (where Δφ/T_(CSLP) represents a frequency offsetof reference clock CSR compared with its nominal value when it is aninteger multiple of the frequency of low power clock signal CSLP).

FIGS. 10-12 are graphs illustrating examples calibration errors(measured in parts per million or ppm) as a function of Δφ whencalculating estimates of a frequency of low power clock signal CSLPaccording to different embodiments of the present invention. In each ofFIGS. 10-12, a frequency of reference clock signal CSR is 26 MHz, afrequency of low power clock signal CSLP is 32 kHz, and a calibrationwindow (over which the calibrations are performed) is 1 ms. In FIG. 10,the graph illustrates errors that may occur when a single final countervalue is used to calculate an estimate of a frequency of low power clocksignal CSLP as discussed, for example, in U.S. Pat. No. 7,272,078. InFIG. 11, the graph illustrates errors that may occur when 10 overlappingcalibration periods are averaged to calculate an estimate of a frequencyof low power clock signal CSLP as discussed above with respect to FIGS.2 and 3. In FIG. 12, the graph illustrates errors that may occur when aregression coefficient (calculated using linear regression) is used tocalculate a frequency of low power clock signal CSLP as discussed abovewith respect to FIGS. 6, 7, 8, and 9. If the ratio between the nominalfrequencies of CSR and CSLP is an integer (so that Δφ=0), the resultingerror may be relatively large. Accordingly, an error may be reduced bychoosing frequencies that do not have such an integer relationship.Moreover, nominal frequencies of CSR and CSLP may be selected to providea relatively low error (e.g., by selecting nominal frequencies of CSRand CSLP so that Δφ=0.1 as shown in FIG. 11). If the CSR frequency is 26MHZ, if the CSLP frequency should be about 32 kHz, and if the CSLPfrequency is selected to be 32.015762 kHz, the nominal ratio may be812.1. For a CSLP frequency of 32.768 kHz, the nominal ratio may be793.46. Moreover, a Δφ of about 0.46 may provide relatively low errorvalues.

FIG. 14 is a block diagram illustrating operations of calibrating lowpower clock signal CSLP using reference clock signal CSR and linearregression as discussed above with respect to FIGS. 7-9. At block 1401,incremented counter values P(i) may be generated at counter 801responsive to edges of reference clock signal CSR. For each cycle of lowpower clock CSLP over a calibration window, calculations may beperformed based on respective incremented counter values at block 1403.At block 1405, a relationship between the reference and low power clocksignals CSLP may be determined using linear regression and thecalculations based on the respective incremented counter values for thedifferent cycles of the low power clock signal CSLP.

At block 1403, performing calculations based on the respectiveincremented counter values may include performing the calculations basedon the respective incremented counter values taken at edges of the sametransition type of the respective cycles of the low power clock signalCSLP. At block 1405, determining the relationship between the referenceand low power clock signals CSR and CSLP using linear regression mayinclude calculating a regression coefficient using the incrementedcounter values from the at least three different cycles of the low powerclock signal CSLP.

FIG. 15 is a flow diagram illustrating operations of calibrating lowpower clock CSLP using reference clock CSR with data from differentwaking periods W as discussed above with respect to FIG. 5. During afirst waking period W, a receiver (of transceiver 115) may be operatedusing reference clock signal CSR at block 1501. For a first calibrationperiod during the first waking period W, a number of edges of referenceclock signal CSR occurring during the first calibration period may bedetermined at block 1503. During a sleep period after the first wakingperiod W, a duration of the sleep period may be timed using low powerclock signal CSLP with reference clock signal CSR turned off at block1505. During a second waking period after the sleep period, the receivermay be operated using the reference clock signal CSR at block 1507. Fora second calibration period during the second waking period, a number ofedges of the reference clock signal CSR occurring during the secondcalibration period may be determined at block 1508. At block 1509, arelationship between reference and low power clock signals CSR and CSLPmay be determined using the number of edges of the reference clocksignal CSR occurring during each of the first and second intervals ofthe first and second wake periods.

Determining the relationship between reference and low power clocksignals CSR and CSLP at block 1509 may include calculating an averagebased on the number of edges of reference clock signal CSR occurringduring the first and second calibration periods. Such an average may becalculated as a moving average so that information from a predeterminenumber of most recent wake periods is considered, for example, using:

${A(k)} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{{X\left( {k - i} \right)}.}}}$

In addition, or in an alternative, an average may be calculated as aweighted average so that information from more recent wake periods isweighted more heavily than information from less recent wake periods.Moreover, information from different wake periods may be combined usingexponential forgetting so that information from less recent wake periodsis weighted exponentially less than information from more recent wakeperiods, for example, using:

A(k)=αX(k)+(1−α)A(k−1), with α<1.

Moreover, multiple calibration periods may be provided during a samewake period. At block 1503, for example, a number of edges of thereference clock signal CSR occurring during a third calibration periodduring the first wake period may be determined, and at block 1508, anumber of edges of the reference clock signal CSR occurring during afourth calibration period during the second wake period may bedetermined. At block 1509, determining the relationship betweenreference and low power clock signals CSLP may include determining afirst representation of the relationship between the reference and lowpower clock signals CSR and CSLP for the first waking period using thenumber of edges of the reference clock signal CSR occurring during thefirst calibration period and the number of edges of the reference clocksignal CSR occurring during the third calibration period. A secondrepresentation of the relationship between the reference and low powerclock signals for the second waking period may be determined using thenumber of edges of the reference clock signal CSR occurring during thesecond calibration period and the number of edges of the reference clocksignal CSR occurring during the fourth calibration period. Afterdetermining the first and second representations of the relationshipbetween the reference and low power clock signals CSR and CSLP, anaggregate representation of the relationship between the reference andlow power clock signals CSR and CSLP may be determined using the firstand second representations.

Determining the relationship between the reference and low power clocksignals at block 1509 may include determining a first representation ofthe relationship between the reference and low power clock signals CSRand CSLP using the number of edges of the reference clock signaloccurring during the first calibration period and the number of edges ofthe reference clock signal occurring during the second calibrationperiod. A second representation of the relationship between thereference and low power clock signals CSR and CSLP may be determinedusing the number of edges of the reference clock signal CSR occurringduring the third calibration period and the number of edges of thereference clock signal CSR occurring during the fourth calibrationperiod. After determining the first and second representations of therelationship between the reference and low power clock signals CSR andCSLP, an aggregate representation of the relationship between thereference and low power clock signals CSR and CSLP may be determinedusing the first and second representations. According to otherembodiments of the present invention, determining the relationshipbetween the reference and low power clock signals at block 1509 mayinclude performing linear regression using the number of edges of thereference clock signal CSR occurring during the first calibrationperiod, during the second calibration period, during the thirdcalibration period, and during the fourth calibration period.

In the drawings and specification, there have been disclosed embodimentsof the invention and, although specific terms are employed, they areused in a generic and descriptive sense only and not for purposes oflimitation, the scope of the invention being set forth in the followingclaims.

1. A method of calibrating a first clock signal using a second clocksignal and a plurality of calibration periods, the method comprising:generating incremented counter values at a counter responsive to edgesof the second clock signal; for at least two of the plurality ofcalibration periods, storing in memory an initial incremented countervalue from the counter at an initial edge of the first clock signal forthe respective calibration period and storing in memory a finalincremented counter value at a final edge of the first clock signal forthe respective calibration period wherein the at least two of theplurality of calibration periods are overlapping with different initialand final edges of the first clock signal; for each of the plurality ofcalibration periods, determining a number of edges of the second clocksignal occurring during the respective calibration period using theinitial and final incremented counter values stored in memory; anddetermining a relationship between the first and second clock signalsusing a sum of a number of edges of the second clock signal occurringduring each of the plurality of calibration periods and using a sum of anumber of first clock signal cycles occurring during each of theplurality of calibration periods.
 2. A method according to claim 1wherein determining the relationship comprises determining a ratio usingthe sum of the number of edges of the second clock signal occurringduring each of the plurality of calibration periods and using the sum ofthe number of first clock signal cycles occurring during each of theplurality of calibration periods.
 3. A method according to claim 1wherein an initial edge of the first clock signal for a first of theplurality of the calibration periods precedes an initial edge of thefirst clock signal for a second of the plurality of the calibrationperiods, wherein the initial edge of the first clock signal for thesecond of the plurality of the calibration periods precedes a final edgeof the first clock signal for the first of the plurality of thecalibration periods, and wherein the final edge of the first clocksignal for the first of the plurality of the calibration periodsprecedes a final edge of the first clock signal for the second of theplurality of the calibration periods.
 4. A method according to claim 1wherein a same number of first clock cycles occur during each of theplurality of calibration periods.
 5. A method according to claim 1wherein the plurality of calibration periods includes k calibrationperiods beginning at k consecutive edges of the same transition type ofthe clock.
 6. A method according to claim 1 wherein generatingincremented counter values comprises generating incremented countervalues at the counter responsive to edges of a same transition type ofthe second clock signal.
 7. A method according to claim 1 wherein afrequency of the first clock signal is not an integer multiple of afrequency of the second clock signal and wherein the frequency of thesecond clock signal is not an integer multiple of the frequency of thefirst clock signal.
 8. A method according to claim 1 wherein the secondclock is coupled to a receiver, the method further comprising: during afirst waking period, operating the receiver using the second clock;during a sleep period after the first waking period, timing a durationof the sleep period using the first clock with the second clock turnedoff; and during a second waking period after the sleep period, operatingthe receiver using the second clock.
 9. A method of calibrating a firstclock signal using a second clock signal, the method comprising:generating incremented counter values at a counter responsive to edgesof the second clock signal; for at least two different edges of thefirst clock signal, performing calculations based on respectiveincremented counter values; and determining a relationship between thefirst and second clock signals using linear regression using thecalculations based on the respective incremented counter values for theat least two different edges of the first clock signal.
 10. A methodaccording to claim 9 wherein performing calculations based on therespective incremented counter values comprises performing thecalculations based on the respective incremented counter values taken atedges of the same transition type of respective cycles of the firstclock signal.
 11. A method according to claim 10 wherein determining therelationship between the first and second clock signals using linearregression comprises calculating a regression coefficient using theincremented counter values from the at least two different edges of thefirst clock signal.
 12. A method according to claim 9 wherein performingcalculations based on the respective incremented counter valuescomprises integrating incremented counter values taken at edges of thesame transition type of different cycles of the first clock signal. 13.A method according to claim 9 wherein generating incremented countervalues comprises generating incremented counter values at the counterresponsive to edges of the second clock signal of the same transitiontype.
 14. A method according to claim 9, wherein at a first edge of thefirst clock signal the counter and first and second adders are set toinitial values, wherein at a second edge of the first clock signal afterthe first edge, an incremented counter value generated by the counter isadded to the initial value of the first adder to generate a second valueof the first adder, and the initial value of the first adder is added tothe initial value of the second adder to generate a second value of thesecond adder, and wherein at a third edge of the first clock signalafter the second edge, an incremented counter value generated by thecounter is added to the second value of the first adder to generate athird value of the first adder, and the second value of the first adderis added to the first value of the second adder to generate a thirdvalue of the second adder.
 15. A method according to claim 9 wherein thesecond clock is coupled to a receiver, the method further comprising:during a first waking period, operating the receiver using the secondclock; during a sleep period after the first waking period, timing aduration of the sleep period using the first clock with the second clockturned off; and during a second waking period after the sleep period,operating the receiver using the second clock.
 16. A method ofcalibrating a first clock signal using a second clock signal coupled toa receiver, the method comprising: during a first waking period,operating the receiver using the second clock signal; for a firstcalibration period during the first waking period, determining a numberof edges of the second clock signal occurring during the firstcalibration period; during a sleep period after the first waking period,timing a duration of the sleep period using the first clock signal withthe second clock signal turned off; during a second waking period afterthe sleep period, operating the receiver using the second clock signal;for a second calibration period during the second waking period,determining a number of edges of the second clock signal occurringduring the second calibration period; and determining a relationshipbetween the first and second clock signals using the number of edges ofthe second clock signal occurring during the first interval and thenumber of edges of the second clock signal occurring during the secondinterval.
 17. A method according to claim 16 wherein determining therelationship between the first and second clock signals comprisescalculating an average based on the number of edges of the second clocksignal occurring during the first calibration period and the number ofedges of the second clock signal occurring during the second calibrationperiod.
 18. A method according to claim 17 further comprising: for athird calibration period during the first waking period, determining anumber of edges of the second clock signal occurring during the thirdcalibration period; and for a fourth calibration period during thesecond waking period, determining a number of edges of the second clocksignal occurring during the fourth calibration period.
 19. A methodaccording to claim 18 wherein determining the relationship between thefirst and second clock signals comprises, determining a firstrepresentation of the relationship between the first and second clocksignals for the first waking period using the numbers of edge of thesecond clock signal occurring during the first calibration period andduring the third calibration period, determining a second representationof the relationship between the first and second clock signals for thesecond waking period using the number of edges of the second clocksignal occurring during the second calibration period and during thefourth calibration period, and after determining the first and secondrepresentations of the relationship between the first and second clocksignals, determining an aggregate representation of the relationshipbetween the first and second clock signals using the first and secondrepresentations.
 20. A method according to claim 18 wherein determiningthe relationship between the first and second clock signals comprises,determining a first representation of the relationship between the firstand second clock signals using the number of edges of the second clocksignal occurring during the first calibration period and the number ofedges of the second clock signal occurring during the second calibrationperiod, determining a second representation of the relationship betweenthe first and second clock signals using the number of edges of thesecond clock signal occurring during the third calibration period andthe number of edges of the second clock signal occurring during thefourth calibration period, after determining the first and secondrepresentations of the relationship between the first and second clocksignals, determining an aggregate representation of the relationshipbetween the first and second clock signals using the first and secondrepresentations.